1. Field of the Invention
The present invention relates generally to a prediction method for monitoring performance of power plant instruments. More particularly, the present invention relates to a prediction method for monitoring performance of power plant during a nuclear power plant operation continually and consistently.
2. Description of the Related Art
In general, all power generating facilities are equipped with a plurality of instruments and obtains various signals in real-time from the plurality of instruments to utilize the obtained various signals in power plant's surveillance and protection systems. Especially, nuclear power plant's measurement channels, related to a safety system, employ multi-instrument concept so as to guarantee accuracy and reliability of measurement signals and also examine and correct power plant instruments at an interval of a nuclear fuel cycle, e.g., approximately 18 months, as read in guidelines for operating technique. All over the world, nuclear power plants have been developing a method for lengthening monitoring and correction periods of unnecessarily-performed instrument correction tasks through a Condition Based Monitoring (CBM) method.
FIG. 1 is a block diagram of a conventional instrument performance regular monitoring system. This system is called an Auto-Associative model. Referring to FIG. 1, the conventional instrument performance regular monitoring system includes a prediction model, a comparison module and a decision logic. The conventional instrument performance regular monitoring system can monitor drift and malfunction of instruments by inputting measuring values into the prediction model, outputting prediction values of the prediction model with respect to an input measurement values, inputting differences between measurement values and the prediction values into the decision logic through the comparison module and continuously monitoring the instruments.
As a method for calculating a prediction value of an instrument, a linear regression method is the most widely used. This method selects signals of other instruments that have a high linear correlation with respect to a signal of an instrument that will be predicted, and obtains a regression coefficient to allow the sum of squares for error of a prediction value and a measurement value to be the minimum. This method can be expressed as the following Equation 1.ΣE2=Σ(Y−Y′)2  <Equation 1>
The linear regression method can predict independent variables with respect to unknown dependent variables once a regression coefficient is determined with already-known dependent and independent variables. However, in an existing linear regression method, if dependent variables have large linear relationships, multicollinearity may occur such that large errors may occur in independent variables with respect to small noise included in dependent variables.
A Kernel regression method is a non-parametric regression method that stores selected measurement data as a memory vector, obtains a weight value of Kernel from Euclidean distance of a training data set in a memory vector with respect to a measurement signal set, and applies the weight value to the memory vector to obtain a prediction value of a measurement instrument without using a parameter such as a regression coefficient, a weight value that optimizes correlation of an input and an output like an existing linear regression method, or a neural network. The non-parametric regression method such like the Kernel regression method has a strong advantage over a model having a nonlinear state of an input/output relationship and signal noise.
The existing Kernel regression method has a calculation procedure as the following 5 steps.
First Step: Training data are represented with a matrix of Equation 2.
                    X        =                  [                                                                      X                                      1                    ,                    1                                                                                                X                                      1                    ,                    2                                                                              ⋯                                                              X                                      1                    ,                    m                                                                                                                        X                                      2                    ,                    1                                                                                                X                                      2                    ,                    2                                                                              ⋯                                                              X                                      2                    ,                    m                                                                                                      ⋮                                            ⋮                                            ⋱                                            ⋮                                                                                      X                                                            n                      trn                                        ,                    1                                                                                                X                                                            n                      trn                                        ,                    2                                                                              ⋯                                                              X                                                            n                      trn                                        ,                    m                                                                                ]                                    <                  Equation          ⁢                                          ⁢          2                >            
where X is a training data matrix stored in a memory vector, n is the number of training data, and m is a number of an instrument.
Second Step: The sum of Euclidian distance of training data for a first instrument signal set is obtained through the following Equation 3.
                                          d            ⁡                          (                                                x                  1                                ,                                  q                  1                                            )                                =                                                    ∑                j                            ⁢                                                (                                                                                    x                        1                                            j                                        -                                                                  q                        1                                            j                                                        )                                2                                                    ⁢                                  ⁢                              d            ⁡                          (                                                x                  2                                ,                                  q                  1                                            )                                =                                                    ∑                j                            ⁢                                                (                                                                                    x                        2                                            j                                        -                                                                  q                        1                                            j                                                        )                                2                                                    ⁢                                  ⁢        ⋮        ⁢                                  ⁢                              d            ⁡                          (                                                x                  trn                                ,                                  q                  1                                            )                                =                                                    ∑                j                            ⁢                                                (                                                                                    x                        trn                                            j                                        -                                                                  q                        1                                            j                                                        )                                2                                                                        <                  Equation          ⁢                                          ⁢          3                >            
where x is training data, q is test data (or, Query data), trn is a number of training data, and j is a number of an instrument.
Third step: A weight value with respect to each of training data sets and given test data sets is obtained through the following Equation 4 including a Kernel function.
                                                                        w                1                            =                                                K                  ⁡                                      (                                          d                      ⁡                                              (                                                                              x                            1                                                    ,                                                      q                            1                                                                          )                                                              )                                                                                                                                          w                2                            =                                                K                  ⁡                                      (                                          d                      ⁡                                              (                                                                              x                            2                                                    ,                                                      q                            1                                                                          )                                                              )                                                                                                            ⋮                                                ⋮                                                                              w                trn                            =                                                K                  ⁡                                      (                                          d                      ⁡                                              (                                                                              x                            trn                                                    ,                                                      q                            1                                                                          )                                                              )                                                                                                          <                  Equation          ⁢                                          ⁢          4                >            
In Equation 4, Gaussian Kernel, used as a weight function, is defined as follows.
      K    ⁡          (      d      )        =            ⅇ              -                  (                                    d              2                                      σ              2                                )                      .  
Forth step: A prediction value of test data is obtained by multiplying a weight value by each training data and dividing its result by the sum of weight values as the following Equation 5.
                                                        y              ⋒                        ⁡                          (                              q                1                            )                                =                                    (                                                x                  trn                                ,                                  j                  *                  w                                            )                        /                          ∑              w                                      ⁢                                  ⁢                                            y              ⋒                        ⁡                          (                              q                1                            )                                =                                    (                                                [                                                                                                              X                                                      1                            ,                            1                                                                                                                                                X                                                      1                            ,                            2                                                                                                                      …                                                                                              X                                                      1                            ,                            j                                                                                                                                                                                        X                                                      2                            ,                            1                                                                                                                                                X                                                      2                            ,                            2                                                                                                                      …                                                                                              X                                                      2                            ,                            j                                                                                                                                                              ⋮                                                                    ⋮                                                                    ⋱                                                                    ⋮                                                                                                                                      X                                                                                    n                              trn                                                        ,                            1                                                                                                                                                X                                                                                    n                              trn                                                        ,                            2                                                                                                                      …                                                                                              X                                                                                    n                              trn                                                        ,                            j                                                                                                                                ]                                *                                  [                                                                                                              w                          1                                                                                                                                                              w                          2                                                                                                                                    ⋮                                                                                                                                      w                          tnr                                                                                                      ]                                            )                        /                          ∑              w                                                          <                  Equation          ⁢                                          ⁢          5                >            
Fifth step: Second to fourth steps are repeated in order to obtain a prediction value with respect to entire test data.
The existing Kernel regression method has a strong advantage over a nonlinear model and signal noise. However, the existing Kernel regression method has disadvantages such as low accuracy due to dispersion increase of an output prediction value compared to a linear regression analysis method. The dispersion increase occurs because the Auto-Associative Kernel Regression (AAKR) method stores selective measurement data as a memory vector, obtains a weight value of Kernel from Euclidean distance of a training data set in a memory vector with respect to a measurement signal set, and applies the weight value to the memory vector to obtain a prediction value of an instrument.